In long term evolution (LTE), which has been standardized in the 3rd generation partnership project (3GPP) and has served as the 3.9-generation radio transmission scheme, a multiple input multiple output (MIMO) technology that performs radio transmission by using a plurality of transmit and receive antennas has been specified for markedly increasing a frequency utilization efficiency as compared with 3rd generation radio transmission schemes.
A spatial multiplexing (SM) technology, which is one of MIMO technologies, can realize an increase in transmission speed without expansion in frequency bandwidth. Also, LTE-advanced (LTE-A), which is an extension of LTE, has been approved as one of 4th generation radio transmission schemes by International Telecommunication Union Radiocommunications Sector (ITU-R), and standardization of LTE-A is actively promoted. In LTE-A, single user MIMO (SU-MIMO), which can provide spatial multiplexing by 8 streams at maximum, is being studied to achieve a peak transmission speed of 1 Gbps in downlink transmission (from base station device to mobile station device). SU-MIMO is MIMO transmission between a base station device having a plurality of transmit antennas, and a single mobile station device having a plurality of receive antennas.
However, the number of receive antennas that can be arranged in the mobile station device is limited. To improve the frequency utilization efficiency, it is required to employ multi-user MIMO (MU-MIMO), in which a plurality of concurrently connected mobile station devices are assumed as a large-scale antenna array and transmit signals from a base station devices to the mobile station devices are spatially multiplexed. MU-MIMO has been already specified in LTE Release 8 (Rel. 8). MU-MIMO employed by the Rel. 8 is a scheme called beam forming in which multiplication of a linear filter is performed in a base station device. Linear MU-MIMO using the linear filter is also expected to be employed in systems of Rel. 9 and later.
In the MIMO transmission, different pieces of transmit data (data streams) are transmitted from the plurality of transmit antennas with the same frequency, and hence a spatial demultiplexing technology is required to detect a desirable signal in the receiver. A technology, which is well known as the spatial demultiplexing technology, is spatial filtering. This is a technology that calculates a linear filter based on the criterion of zero-forcing (ZF) or minimum mean square error (MMSE) from a channel matrix which represents channel state information (CSI) between the transmitter and the receiver, and performs multiplication of the linear filter in the receiver.
However, the spatial filtering has a spatial demultiplexing performance which is markedly degraded as compared with maximum likelihood detection (MLD), which is an optimal spatial demultiplexing technology, although the spatial filtering only requires a small computation amount. In particular, as a spatial correlation increases in a channel, the degradation in performance increases.
In recent years, to increase the spatial demultiplexing performance of the spatial filtering, application of a lattice reduction (LR) technology to the MIMO transmission is receiving attention, and the application is discussed in NPL 1, NPL 3, etc. With the LR technology, a channel matrix is multiplied by a unimodular matrix and is transformed into a channel matrix with high orthogonality. Accordingly, the spatial demultiplexing performance of the spatial filtering can be increased.